{"paper":{"title":"The Dirichlet Process with Large Concentration Parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Luai Al Labadi, Mahmoud Zarepour","submitted_at":"2011-09-24T12:54:11Z","abstract_excerpt":"Ferguson's Dirichlet process plays an important role in nonparametric Bayesian inference. Let $P_a$ be the Dirichlet process in $\\mathbb{R}$ with a base probability measure $H$ and a concentration parameter $a>0.$ In this paper, we show that $\\sqrt {a} \\big(P_a((-\\infty,t]) -H((-\\infty,t])\\big)$ converges to a certain Brownian bridge as $a \\to \\infty.$ We also derive a certain Glivenko-Cantelli theorem for the Dirichlet process. Using the functional delta method, the weak convergence of the quantile process is also obtained. A large concentration parameter occurs when a statistician puts too m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5261","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}